The classification of smooth well-formed Fano weighted complete intersections

Abstract

We show that the set of families of smooth well-formed Fano weighted complete intersections admits a natural partition with respect to the variance var([Formula: see text]) = coind([Formula: see text]) - codim([Formula: see text]). Moreover, we obtain the classification of smooth well-formed Fano weighted complete intersections of small variance. We also prove that the anticanonical linear system on a smooth well-formed Fano weighted complete intersection of anticanonical degree one is never base-point-free.